UC-NRLF 


STUDY 


ON 


RESERVOIR    WALLS 


BY 


J.  B.  KRANTZ, 

INGENIEUR  EN  CHEF  DES  FONTS  ET  CHAUSS&ES. 


TRANSLA  TED  FROM  THE  FRENCH 


BY 

F.  A.  MAHAN, 

CAPTAIN   OF   ENGINEERS,    U.    S.    ARMY. 


ILLUSTRATED  BY  34  PLATES,  COMPARING  SECTIONS  OF  DAMS  ACTUALLY 
CONSTRUCTED  WITH  THE  PROFILE-TYPES. 


NEW  YORK : 

JOHN    WILEY     &     SONS, 
15  ASTOR  PLACE. 

1883. 


UFI7BESIT7 


COPYRIGHT,  1883,  BY 
F.  A.  MAHAN. 


HESS  OF    J.    J.  LITTLE   8.  CO., 


AUTHOR'S  PREFACE. 


THE  study  now  published  was  made  during  the 
year  1865.  It  bears  the  marks  of  the  duties  brought 
upon  me  by  the  service  of  the  department  of  the  Ar- 
deche,  of  which  I  was  then  chief  engineer. 

Ordered  to  Paris,  and  placed  successively  in  charge 
of  a  hard  task  at  the  Exposition  and  of  an  important 
navigation  service,  I  laid  my  almost  finished  study 
aside  up  to  the  present  time. 

Since  1865  several  articles  have  been  written  on 
the  walls  of  reservoirs.  I  can  especially  mention  the 
remarkable  documents  published  in  the  Annales  des 
Pouts  et  Chaussees  (September  and  October,  1866)  by 
MM.  Graeff  and  Delocre. 

I  am  certainly  very  well  content  to  find  that  my 
views  agree  with  those  of  the  excellent  engineers 
whose  names  I  have  just  mentioned.  Still  I  cannot 
but  feel  that  their  work  takes  away  from  mine,  with 
its  theoretical  interest,  a  part  of  its  practical  useful- 
ness. My  first  motion  was,  therefore,  to  shut  it  up  in 
my  drawer. 

3 


4  AUTHORS    PREFACE. 

After  some  reflection  I  decided  to  publish  it.  In 
fact,  it  seems  to  me  that  this  study,  now  shorn  of  all 
scientific  appearance,  and  reduced  to  a  sort  of  practi- 
cal formulary,  may  still  render  to  engineers  the  ser- 
vices that  I  expected  from  it  myself  at  a  certain  time. 

If  this  hope  be  realized,  my  object  will  be  wholly 
accomplished. 

J.  B.  KRANTZ. 

PARIS,  January,  17,  1870. 


TRANSLATOR'S  PREFACE. 


IN  preparing  this  work  for  the  American  press,  the 
translator  has  been  guided  by  the  same  motive  which 
led  M.  Krantz  to  publish  it,  viz  :  the  hope  that  as 
a  mere  practical  formulary,  it  might  be  of  use  to  en- 
gineers whose  duties  lead  them  to  the  construction  of 
reservoir  walls. 

Since  M.  Krantz  wrote  his  work,  M.  Pelletreau  has 
written  a  series  of  excellent  articles  in  the  following 
numbers  of  the  Annales  des  Fonts  et  Ckaussees:  1876, 
second  half  year  ;  1877,  second  half  year  ;  1879,  ^rst 
half  year.  Those  desiring  to  study  this  subject  theo- 
retically will  do  well  to  add  these  articles  to  those 
mentioned  by  M.  Krantz. 

As  the  mere  transformation  of  the  metric  denomin- 
ations into  the  English  would  cause  the  quantities  in 
the  drawings  and  tables  to  appear  wholly  arbitrary, 
I  have  thought  it  best  to  retain  the  metric  values, 
while  giving  in  all  cases  their  English  equivalents. 
On  the  drawings  the  English  denominations  are 
above  the  lines,  and  the  metric  below. 

F.  A.  M. 

DAVIS  ISLAND  DAM, 

August  28,  1882. 

5 


STUDY 


ON  THE 


WALLS    OF    RESERVOIRS. 


I. 

GENERAL    CONSIDERATIONS    ON    THE    USEFULNESS   OF 
TAKING    GOOD    CARE    OF    WATER. 

AMONG  the  measures  that  may  contribute  to  the  in- 
crease of  production,  the  complete  husbanding  of 
water  has  always  been  pointed  out  as  one  of  the  most 
effective. 

In  fact  water  gives  at  once  a  powerful  stimulant  to 
vegetation  and  a  cheap  motive  power. 

The  influence  of  water  on  vegetation  is  too  well 
known  for  it  to  be  necessary  to  speak  of  it  here.  We 
need  only  say  that  but  little  land  exists  which  may  not 
become  productive  if  watered  ;  that  there  is  no  soil  so 
fertile  that  its  productiveness  cannot  be  increased  by 
irrigation.  In  short  and  in  general  terms  we  may 
say  that  scarcely  any  barren  lands  exist  except  those 
absolutely  deprived  of  water,  and  that  the  maximum 
of  production  can  only  be  obtained  by  watering. 

In  our  day,  the  great  industries  use  steam  as  the 

7 


8  STUDY    ON    RESERVOIR   WALLS. 

motive  power,  it  being  produced  by  means  of  coal. 
But  mineral  fuel  is  not  recreated. 

The  great  reserves  placed  by  nature  at  our  disposal 
will  certainly  be  sufficient  for  our  generation  and  for 
those  which  immediately  follow  it.  We  may,  how- 
ever, foresee  and  even  calculate  the  time  when  this 
precious  resource  will  be  wanting  in  Europe.  On  this 
account  it  must  henceforth  be  economized  either  by 
better  arrangements  and  a  better  control  of  our  fires,  or 
else  by  searching  nature  and  utilizing  the  auxiliary 
forces  which  may,  for  certain  purposes,  replace  steam. 

Among  these  forces,  the  fall  of  water  holds  a  promi- 
nent position  on  account  of  its  economy  and  on  account 
of  the  many  cases  in  which  it  can  be  used  to  advantage. 

The  unceasing  motion  of  aerial  circulation  is  con- 
stantly raising  and  carrying  immense  quantities  of 
water  taken  from  the  ocean  and  spreading  them  over 
the  principal  chains  of  mountains.  Thence  they  return 
to  the  sea  through  various  brooks  and  rivers  to  be 
again  taken  up  and  carried  back.  This  incessant 
creation  of  force  seems  to  be  intimately  connected 
with  our  planet  and  will  only  come  to  an  end  when  it 
does.  Wisely  looked  after,  it  will  always  be  one  of 
the  most  precious  resources  for  industrial  pursuits. 

If  water,  as  a  motive  power  and  as  a  stimulant  for 
vegetation,  have  a  preponderating  part,  its  usefulness 
from  another  point  of  view  is  not  less.  It  has  become 
the  basis*  of  hygiene  and  domestic  comfort,  and 
every  day  larger  supplies  are  called  for  in  our  cities. 


STUDY    ON    RESERVOIR   WALLS.  9 

The  small  ration  of  water  that  sufficed  for  our  fa- 
thers is  no  longer  enough  for  us.  In  vain  is  it  largely 
increased ;  it  is  always  less  than  the  requirements  of  the 
people. 

Needs  of  this  kind  have  become  so  urgent  that,  in 
countries  where  the  grouping  of  the  population  is  not 
trammeled  by  old  customs  or  by  necessities  of  posi- 
tion, cities  are  seen  to  spring  up  at  those  points  where 
large  supplies  of  water  satisfy  new  demands. 

But  if,  from  all  these  points  of  view,  the  wise  caring 
for  water  becomes  more  and  more  desirable,  it  must  also 
be  noticed  that  it  becomes  more  and  more  difficult. 

As  a  consequence  of  very  complex  causes,  of  which 
the  principal  seem  to  be  the  cutting  down  of  forests 
and  the  cultivation  of  the  soil,  the  regimen  of  our 
streams  is  becoming  more  and  more  unsteady. 

Dry,  or  very  nearly  so,  in  the  summer,  our  rivers 
contain  in  the  wet  season  large  volumes  of  water.  If 
their  slope  be  great,  they  become  real  torrents  which 
scatter  ruin  and  desolation  along  their  Nbanks. 

The  small  summer  discharge  does  not  at  all  show  a 
lack  of  volume  in  the  water  that  falls.  Far  from  it.  The 
department  of  the  Ardeche,  toward  which  my  thoughts 
turn  while  writing  these  lines,  is  one  of  those  in  which 
this  giving  out  of  the  springs  in  summer  is  most  re- 
markable, and  still  it  is  of  all  the  departments  of 
France  the  most  widely  endowed  with  rains.  The 
high  chains  of  the  Tanargue,  the  Coyrons  and  the 
Mezen  stop,  chill  and  condense  the  winds  saturated 


IO  STUDY    ON    RESERVOIR   WALLS. 

with  moisture  from  the  Mediterranean,  and  force  them 
to  pour  out  great  masses  of  water  on  the  ground. 

Observations  made  at  Mezillac,  in  the  midst  of  the 
Coyrons  chain,  and  at  Montpezat,  show  a  mean  an- 
nual rainfall  of  i  m.  91  (75.6  inches).  At  Joyeuse,  on 
November  9,  1827,  the  rain  that  fell  during  21  hours 
reached  the  enormous  height  of,  om.  729  (28.7  inches). 

The  quanity  of  rain  that  falls  in  the  Ardeche  is 
therefore  very  great,  but  on  the  other  hand  it  is  very 
unequally  distributed  over  the  different  parts  of  the 
year.  The  same  may  be  said  of  many  of  the  depart- 
ments of  the  south  of  France  and  of  Algiers. 

This  unequal  distribution  of  rain  causes  two  terrible 
scourges — floods  and  prolonged  droughts.  The  former 
scatters  more  ruin  in  a  short  time  and  strikes  the  minds 
of  the  people  more  than  the  other.  The  second,  less 
destructive  in  appearance,  covers  a  greater  extent  of 
territory  and  really  does  much  more  harm. 

A  remedy  has  long  been  sought  for  these  natural 
scourges,  and  it  has  been  thought  to  be  found  in  the 
construction  of  vast  stores  of  water  which  will  substi- 
tute a  rational  husbanding  for  the  capricious  and  often 
ill-regulated  supplies  brought  by  atmospheric  agents. 

It  is  not  uninteresting  to  see  within  what  limits,  on 
this  point,  man  may,  with  the  resources  furnished  by  his 
own  industry,  overcome  the  infirmities  of  his  condition. 

There  can  be  no  doubt  of  this  so  far  as  droughts 
are  concerned.  The  stores  that  place  at  the  disposal 
of  agriculture  and  industry,  for  use  during  dry  spells, 


STUDY    ON    RESERVOIR   WALLS.  II 

the  surplus  put  away  during  the  rainy  season,  correct 
very  effectively  the  inequality  in  nature's  supplies. 

This  is  manifest  in  principle,  and,  moreover,  -expe- 
rience has  shown  that  this  remedy  is  in  so  far  very 
effective  that  the  water  thus  stored  does  not  cost  more 
than  agriculture  and  industry  can  afford  to  pay. 

From  the  earliest  times  there  have  been  built,  in 
India  and  Ceylon,  reservoirs  which  have  called  forth 
about  them  real  oases  of  greenness  and  fertility. 

Wherever,  by  reason  of  the  frequent  revolutions  of 
the  East,  these  useful  monuments,  the  fruits  of  peace 
and  the  legacy  of  a  provident  administration,  were 
destroyed  or  perished  through  want  of  being  kept  in 
repair,  the  rich  cultivation  which  their  existence  called 
forth  disappeared  with  them.  Jungles  and  banks  of 
sand  took  possession  of  the  ground  only  to  disappear 
again  when  the  reservoirs  were  rebuilt. 

Demonstration  on  this  point  is  complete,  and  the 
splendid  works  for  storing  water  and  for  irrigation  exe- 
cuted in  the  south  of  Spain,  furnish  an  example  nearer 
to  our  doors  but  not  more  conclusive  as  to  the  effect- 
iveness of  reservoirs  against  long  continued  droughts. 

In  his  very  remarkable  study  on  the  floods  of  the 
Loire,  M.  Comoy  shows  that  the  height,  and  conse- 
quently the  destructive  effects  of  floods  can  be  much 
lessened  by  building  in  the  upper  parts  of  the  valleys 
of  the  Loire  and  the  Allier  85  reservoirs,  having  a 
total  capacity  of  592  millions  of  cubic  metres  (20,904 
millions  of  cubic  feet). 

'^'OP 

"fflUVHRSITy 


12  STUDY    ON    RESERVOIR    WALLS. 

It  is  difficult  to  doubt  the  justice  of  M.  Comoy's 
observations  and  the  exactness  of  the  consequences 
that  he  deduces  therefrom.  Still,  at  bottom,  all  this 
ingenious  system  rests  on  a  sort  of  control  that  the 
reservoirs  must  establish  by  delaying  the  arrival,  at 
certain  points,  of  the  rises  of  some  of  the  tributaries. 
But  this  presupposes  a  very  nearly  established  order 
in  the  times  of  the  rises  of  these  tributaries,  and,  con- 
sequently, of  the  atmospheric  phenomena  which  cause 
them.  Now  this  order  cannot  be  absolute.  Nothing 
proves  that  it  may  not  be  changed  or  even  inverted, 
whence  it  follows  that  the  delay  in  some  streams  may 
cause  troublesome  coincidences  of  the  maxima  of  rises, 
and  aggravate  in  some  part  of  the  river  the  destruct- 
ive effects  which  it  was  thought  to  lessen. 

Assuming  even  that  the  spontaneous  working  of  the 
projected  reservoirs  will  always  exert  the  moderating 
action  expected  from  them,  it  may  be  asked  whether 
the  capital  engaged  in  these  colossal  structures  might 
not  be  differently  and  more  efficaciously  used.  Might 
not  the  interest  be  more  simply  divided  among  the 
riparian  owners  who  are  reached  by  the  floods  ?  Bet- 
ter still,  would  it  not  answer  to  keep  up,  with  this  in- 
terest and  the  insurance  premiums  voluntarily  payed 
in  by  the  riparian  owners  themselves,  a  large  mutual- 
assistance  fund  ?  The  disasters  caused  by  floods,  which 
after  all  only  come  at  long  intervals,  would  in  this  way 
be  probably  sufficiently  covered. 

I  am  free  to  confess  that  this  system  of  cure  substi- 


STUDY   ON    RESERVOIR   WALLS.  13, 

tuted  for  the  one  proposed  is  less  flattering  to  human 
pride ;  but,  after  all,  what  does  it  matter  if  the  result 
sought  be  brought  about  without  too  many  sacrifices ! 
So  long  as  the  remedy  is  effective,  and  as  it  properly 
repairs  the  damages  done  by  the  flood,  we  need  not 
be  too  particular  about  inquiring  whether  it  comes 
from  the  methods  of  economists  or  from  the  art  of 
the  engineer. 

Assuming  that  the  system  so  carefully  studied  by 
M.  Comoy  be  fully  effective  on  the  Loire  ;  assuming, 
moreover,  that  it  be  not  better  to  substitute  a  system 
of  mutual  insurance,  we  may  still  be  allowed  to  ask 
whether  the  same  methods  will  everywhere  produce 
the  same  results.  This  may  be  doubted,  and,  for  my 
part,  certain  facts,  such  as  the  one  I  am  going  to  men- 
tion, do  not  give  me  much  confidence  on  this  point. 

The  dams  projected  for  the  valley  of  the  Ardeche, 
to  prevent  the  return  of  the  great  floods  of  this  river, 
gave  a  total  capacity  of  60  millions  of  cubic  metres  (212 
millions  of  cubic  feet).  To  build  them  would  have 
required  great  amounts  of  money,  and  the  taking 
possession  of  large  tracts  of  fertile  land  in  a  country 
which  possesses  but  little.  More  could  scarcely  be  done, 
and  still  it  was,  as  will  be  seen,  wholly  insufficient* 

The  River  Ardeche  discharged  from  midnight  of  Sep- 
tember Qth,  1857,  to  noon  of  the  next  day,  86,400,000 
cubic  metres  (305  millions  of  cubic  feet),  and  in 

*  See  the  article  by  M.  Marchegay  in  the  Annales,  1861,  ist  half  year,  pp.  I 
to  16. 


14  STUDY    ON    RESERVOIR   WALLS. 

the  succeeding  22  hours  there  was  a  further  dis- 
charge of  351,936,000  cubic  metres  (12,427,860,000 
cubic  feet.) 

Assuming  all  the  reservoirs  to  have  been  absolutely 
empty  on  the  morning  of  September  8th,  they  would 
have  been  filled  during  the  8th  and  Qth,  and  from  the 
loth  would  have  ceased  to  act. 

The  rise  of  September  gth  would  have  been  les- 
sened ;  that  of  the  loth,  which  was  very  destructive, 
would  have  preserved  all  its  frightful  violence. 

It  is  true  that  M.  Comoy  assigns  to  his  reservoirs  a 
more  complex  task  than  that  of  mere  storage.  He 
assumes  that  when  open  at  the  gorge  they  discharge 
water  while  they  still  receive  it,  and,  from  the  begin- 
ning, only  hold  a  part  of  what  comes  into  them.  In 
this  way  they  give  up  during  the  falling  period  of  the 
flood  the  water  accumulated  during  the  rise.  But  in 
the  present  case,  this  ingenious  working  would  have 
been  of  little  avail.  The  reservoirs  would  have  been 
half  filled  during  the  9th,  and  would  only  have  been 
able  to  withdraw  from  the  discharge  of  the  loth  about 
30  millions  of  cubic  metres  (106  millions  of  cubic 
feet),  which  would  not  have  been  enough  to  sensibly 
change  the  height  of  the  water  and  the  damages 
caused  thereby. 

Hence  it  would  be  imprudent,  in  my  opinion,  to 
assume  at  present  that  we  possess  any  preventive 
which  can  be  generally  used,  and  which  is  certainly 
effective  against  the  scourge  of  inundations.  This 


STUDY    ON    RESERVOIR   WALLS.  15 

scourge  often,  if  not  always,  exceeds  our  knowledge 
and  resources. 

This  is  not  the  case  with  prolonged  droughts. 
Wherever  they  occur,  so  long  as  it  does  not  arise  from 
a  radical  insufficiency  in  the  amount  of  rain  annually 
pourecfl  upon  the  ground,  but  from  excessive  irregu- 
larity in  its  distribution,  the  remedy  has  long  been 
found,  and  we  may  wonder  that  it  has  not  been 
oftener  used. 

In  fact,  it  is  enough  to  store  up  the  excess  of  water 
that  falls  during  the  wet  season,  and  to  keep  it  for 
the  dry. 

This  storing  up  is  one  of  the  most  useful  and  indus- . 
trially  productive  operations  that  can  be  performed. 

I  have  already  said  this  before,  but  a  few  facts  and 
figures,  taken  from  the  department  of  the  Ardeche, 
allow  me  to  make  myself  more  clear  on  this  point. 

Sloping  to  the  Rhone  on  the  east,  the  department 
of  the  Ardeche  rests  on  the  west  against  the  hills  of 
the  Cevennes  and  the  last  abutments  of  the  Au- 
vergne.  It  is  like  a  gigantic  inclined  plane,  of  which 
the  lower  edge  is  formed  by  the  Rhone  at  about  85 
metres  (279  feet)  above  the  level  of  the  sea,  and  of 
which  the  upper  edge  reaches  altitudes  of  1,200,  1,400, 
and  even  1,750  metres  (3,900,  4,600,  and  6,750  feet), 
at  M£zen  above  the  same  level.  The  width  of  the  in- 
clined plane  is  about  60  kilometres  (nearly  40  miles). 

In  rolling  from  these  heights  to  the  Rhone  this 
water  develops  a  very  considerable  motive  power, 


1 6  STUDY    ON    RESERVOIR   WALLS. 

which  is  already  utilized,  but  from  which  greater  ser- 
vice might  be  obtained. 

If  the  fall  of  the  water  be  limited  to  1,000  metres 
(3,300  feet),  we  find  that  not  more  than  2,400  cubic 
metres  (8,500  cubic  feet)  of  water  are  required  to 
create  in  the  fall  the  same  work  that  a  one-horse-power 
engine  could  produce,  if  in  constant  operation  during 
the  entire  year.  In  this  proportion,  the  construction 
of  a  reservoir  having  a  capacity  of  2,400,000  cubic 
metres  (85,000,000  cubic  feet)  at  the  top  of  the  moun- 
tain is  equivalent  to  creating  a  force  of  a  1,000  horse- 
power engine. 

Figuring  out  all  the  expenses,  we  find  that,  under 
ordinary  circumstances,  a  cubic  metre  of  water  stored 
in  the  reservoirs  cost  about  o.oi5f.  ($0.000083  per 
cubic  foot).  This  supposes  that  the  reservoir  is  only 
filled  once  a  year  ;  if  it  be  filled  twice,  the  cost  is 
reduced  to  o.oo75f.  ($0.000042  per  cubic  foot)  ;  it 
may  even  come  as  low  as  o.oo5f.  ($0.000027  per  cubic 
foot)  if  it  be  filled  three  times.  With  the  quantity  of 
rain  that  habitually  falls  on  the  high  mountains  of  the 
Ardeche,  two  and  three  fillings  a  year  may  frequently 
be  had  ;  but  counting  only  on  one,  the  gross  cost  per 
horse-power  only  reaches  36  francs  ($7.20)  per  year, 
which  is  certainly  not  dear. 

If  it  be  added  that  this  water,  filtered  over  beds  of 
basalt  or  granite,  is  generally  extremely  pure,  and 
thoroughly  fit  for  currying  leather,  dyeing  wools, 
bleaching  linen  and  paper,  the  great  industrial  in- 


STUDY    ON    RESERVOIR   WALLS.  17 

terest  attaching  to  its  use  will  have  been  pointed 
out. 

Considerations  of  another  kind,  taken  in  the  same 
localities,  show  that  this  good  care  of  water,  every- 
where so  desirable,  may  sometimes  become  a  necessity 
of  the  highest  order. 

In  1864  the  department  of  the  Ardeche  contained 
1,440  hydraulic  works,  used,  in  general,  for  milling 
and  for  spinning  of  silks.  Few  in  number  and  very 
small  in  the  beginning,  these  establishments  have 
multiplied  out  of  proportion  on  some  streams,  and  in 
perfecting  their  plant  have  needed  a  greater  motive 
power — that  is,  a  greater  supply  of  water. 

During  three-quarters  of  the  year  the  water  is  suf- 
ficient for  the  factories,  and  the  owners  live  in  peace. 
But  when  the  summer  sets  in,  the  rivers  only  contain 
a  thin  stream  of  water  in  the  midst  of  a  wide  bed. 
Penury  begins,  and  with  it  come  fierce  competition 
and  lawsuits  before  all  the  courts. 

Armed  with  their  laws  and  regulations,  the  courts 
intervene,  but  almost  always  without  success.  What- 
ever firmness  they  display,  with  whatever  sagacity 
they  apply  the  salutary  prescriptions  of  the  law,  the 
struggle  and  anarchy  hold  on.  The  force  of  circum- 
stances carries  away  both  the  careful  equity  of  the 
judges  and  the  real  good  will  of  the  people  them- 
selves. It  would  be  difficult  to  tell  the  amount  of 
strength,  intelligence,  work  and  money  spent  in  these 
constantly  renewed  struggles,  and  the  unceasing 


1 8  STUDY    ON    RESERVOIR   WALLS. 

trouble  that  they  bring  about  in  the  relations  of  the 
inhabitants. 

Taking  care  properly  of  the  water,  by  keeping  for 
the  summer  a  part  of  the  winter's  surplus,  would  do 
more  to  pacify  interests,  to  set  at  rest  internal  dis- 
cords, than  the  wisest  rules,  how  carefully  soever  they 
be  applied. 

Pisciculture. — In  the  Ardeche,  as  elsewhere,  much 
attention  is  given  to  pisciculture.  This  attention  is 
the  more  legitimate,  as  the  rivers  of  this  department 
seem  to  be  well  adapted  to  rearing  fish,  and  contain 
some  excellent  kinds. 

But  when  summer  comes,  all  these  fishes  are 
obliged  to  take  refuge  in  holes  where  a  little  water 
still  remains.  They  there  develop  poorly,  being  too 
much  confined,  and  become  an  easy  prey  to  all  ma- 
rauders. 

The  temptation  is  such  that  all  contrivances, 
whether  permitted  or  not,  all  methods,  even  poisoning, 
are  used  to  destroy  them,  and  at  the  end  of  each  sum- 
mer they  have  almost  entirely  disappeared. 

By  keeping  a  little  water  in  the  rivers  during  the 
dry  season,  an  end  would  be  put  to  this  unintelligent 
destruction. 

Thus,  from  whatever  point  of  view  we  look  at  it, 
the  proper  caring  for  water  appears  as  one  of  the 
most  useful  works  that  can  be  done.  It  is  not  rash 
to  think  that  when  the  needs  for  roadways  shall  have 


STUDY   ON    RESERVOIR   WALLS.  1 9 

ceased  to  be  urgent,  which  cannot  be  far  away,  public 
attention  will  be  turned  in  this  direction. 

Is  it  necessary  to  say  it?  Water  can  only  be  prop- 
erly stored  by  means  of  deep  ponds  set  in  the  upper 
parts  of  valleys.  There  is  found,  as  a  rule,  the 
greatest  facility  for  building  the  dams  of  reservoirs. 
It  is  there,  also,  that  the  stored-up  water  may  do  the 
most  good,  since,  in  coming  down,  it  is  found  at  all 
stages,  either  as  a  motive  power  or  as  an  irrigator. 

The  preceding  considerations  will  doubtless  appear 
somewhat  ambitious  as  a  preamble  to  a  note  intended 
to  set  forth  the  best  shape  to  be  given  to  reservoir 
walls. 

Still,  as  these  are  the  considerations  which  led  me 
to  the  study  which  I  now  give  to  the  public,  I  thought 
that  they  might  also  be  of  some  interest  to  the  reader, 
and  assist  him  in  enduring  the  dry  examination  of 
the  technical  considerations  which  are  to  follow. 


II. 


RESERVOIR   WALLS. 

Glance  at  the  walls  of  existing  dams. — At  first  at- 
tributed to  the  Moors,  whose  solicitude  for  agricul- 
tural works,  and  consequently  for  the  good  care  of 
water,  is  well  known,  the  great  reservoirs  of  the 
south  of  Spain  seem  to  be  a  decidedly  Spanish 
creation. 


20  STUDY    ON    RESERVOIR   WALLS. 

It  is  a  glorious  token,  which  Spain  can  lay  claim  to 
with  just  pride,  because  these  immense  works  show  a 
great  persistence  of  views  and  a  marked  appreciation 
of  the  real  conditions  of  richness  for  a  country  in  the 
people  who  paid  for  them  out  of  their  savings,  and 
who  resorted,  in  order  to  build  them,  to  the  powerful 
lever  of  association. 

The  kings  of  Spain  themselves,  taken  up  as  they 
were  with  their  external  struggles  and  with  their  con- 
quests in  two  worlds,  not  only  placed  no  obstacles  in 
the  way  of  these  great  works  of  peace,  but  even  gave 
them  great  encouragement.  They  should  be  equally 
praised. 

Here  eulogy  must  necessarily  stop,  because  the 
execution  of  the  walls  of  the  dams  was  not  equal  to 
the  high  economic  conceptions  that  gave  birth  to  the 
projects. 

In  fact,  it  is  easy  to  see,  in  the  great  size  and  im- 
mense extent  of  the  masses  employed,  a  complete 
lack  of  understanding  of  the  intensity  and  distribu- 
tion of  the  forces  to  be  overcome.  Not  knowing  how 
to  find  the  direction  of  these  forces,  or  to  calculate 
their  intensities  exactly,  they  doubled  or  trebled  the 
necessary  volumes  of  masonry,  and,  instead  of  the 
graceful  and  elegant  structures  at  which  we  have  now 
arrived,  they  built  prodigious  walls  that  excite  aston- 
ishment, and  show  a  small  amount  of  skill  combined 
with  an  immense  energy  of  will. 

The  figures  accompanying   this   note   show   that, 


STUDY    ON    RESERVOIR   WALLS.  21 

however  sharp  it  may  be,  this  criticism  is  not  too 
severe,  and  that  if  the  walls  of  the  Spanish  reservoirs 
are  respectable  through  their  age,  imposing  through 
their  mass,  they  still  belong,  in  reality,  to  the  infancy 
of  art.  It  is  in  vain  that,  with  unthinking  enthusiasm, 
it  has  been  desired  to  call  the  great  wall  of  Alicante, 
the  principal  one  among  them,  by  the  name  of  Her- 
rera ;  the  name  of  the  illustrious  architect  of  the  Es- 
corial  has  nothing  to  gain  by  this  tardy  recognition. 

More  soberly  conceived,  more  wisely  built,  the 
reservoir  walls  constructed  in  France  for  the  water 
supply  of  the  canals  have  not  the  imposing  air  of  the 
Spanish  works,  but  they  show  a  clearer  conception  of 
the  forces  to  be  overcome  and  greater  care  in  regard 
to  economy.  In  a  word,  they  show  a  real  advance  in 
the  art  of  building. 

Still  they  are  not  irreproachable — far  from  it. 
Among  those  which  I  might  mention  is  the  Gros-Bois 
wall  (Fig.  30)  for  example,  which,  now  not  very 
strong,  would  very  nearly  satisfy  all  conditions  of 
stability  if  it  were  turned  around ;  that  is,  if  the  up- 
stream side  were  down-stream  and  the  reverse. 

A  new  era  for  the  construction  of  reservoir  walls 
dates  from  the  article  published  by  Sazilly  in  the 
Annales  des  Pouts  et  Chans  sees  (1853,  2<^  na^  year). 
With  rare  insight,  Sazilly  was  able  to  discern  the  na- 
ture, amount  and  direction  of  the  various  forces 
which  act  on  reservoir  walls  at  the  different  periods 
of  filling  the  basins.  From  them  he  deduces  ra- 


22  STUDY   ON    RESERVOIR   WALLS. 

tional  forms  to  be  given  to  constructions  of  this 
sort. 

I  take  the  liberty  of  not  wholly  sharing  Sazilly's 
opinion  and  of  saying  that  his  profiles  leave  something 
to  be  desired.  But  I  cannot  speak  too  highly  of  the 
esteem  in  which  I  hold  his  excellent  work.  Further- 
more, the  engineers  of  the  Fonts  et  Chaussees,  who, 
since  that  time,  have  had  to  construct  reservoir  walls 
have  been  evidently  inspired  by  Sazilly's  ideas.  It  is 
easy  to  see  this  in  the  very  correct  profiles  of  the  wall  of 
Ternay,  the  Furens  and  the  Habra,  which  leave  far 
behind  them  any  previously  built. 

Taking  up  the  subject  where  Sazilly  left  it,  MM. 
Graeff  and  Delocre  published  in  the  Annales  des  Fonts 
et  Chaussees  (September  and  October,  1866)  two  very 
good  articles  which,  in  my  opinion,  leave  nothing  to 
be  desired.* 

The  theoretical  study  of  reservoir  walls  may  there- 
fore be  regarded  as  definitely  fixed  except  in  some 
points  of  detail.  Constructors  have  now  little  to  do 
but  follow  the  track  so  clearly  marked  out. 

Choice  of  the  system  of  dam. — Three  principal  sys- 
tems have  been  used  in  building  dams  of  large  reser- 
voirs :  viz.,  earthen  embankments,  masonry  walls 
and  walls  and  embankments  together. 

This  last  system  has  rarely  been  successful.    It  has 

*  See  also  articles  by  M.  Pelletreau  in  the  Annales  for  1876,  1877,  1879. 


STUDY   ON  RESERVOIR   WALLS.  23 

all  the  defects  of  both  the  others  and  seems  to  be 
much  the  most  expensive.  I  therefore  mention  it  only 
to  call  it  to  mind. 

Built  principally  in  England,  Scotland  and  the  cen- 
tre of  France,  earthen  dams  seem  to  be  most  useful 
when  the  ground  is  not  adapted  for  the  foundations 
of  walls.  They  work  better  in  mild,  damp  climates 
than  in  dry  and  warm  where  the  earth  of  which  they 
are  made  is  apt  to  crack  and  form  fissures ;  but  deep 
ponds  cannot  be  made  with  them  without  great  cost. 

In  fact,  the  volume  of  earth  to  be  used  increases 
rapidly  when  the  height  increases  ;  and,  as  the  em- 
bankments must  be  made  with  extreme  care  and  with 
selected  earth,  it  does  not  appear  that  there  is  any 
advantage  in  building  earthen  dams  beyond  a  height 
of  30  metres  (100  feet). 

Climatic  conditions,  the  nature  of  the  ground,  the 
facilities  which  it  offers  for  the  construction  of  mason- 
ry, have  generally  given  the  preference  to  walls  over 
earthen  dams  in  Spain  and  the  south  of  France. 
More  easily  and  quickly  built,  soon  water-tight,  free 
from  settling,  the  wall  deserves  the  preference,  espe- 
cially for  great  heights,  provided  always  that  the 
ground  admits  of  its  being  firmly  founded. 

Moreover,  it  is  easy  to  see  that  the  costs  of  these 
two  styles  of  constructions  do  not  differ  so  much  as 
would  appear  at  first  glance. 

Embankments  should  always  be  made  of  carefully 
selected  earth,  sufficient  but  not  too  much  clay  and 


24  STUDY    ON    RESERVOIR   WALLS. 

sandy,  but  not  in  excess.  It  should  be  carefully 
cleansed,  before  use,  of  pebbles,  roots  and  easily  de- 
composed bodies. 

Finally,  it  should  be  carefully  laid  in  successive  lay- 
ers of  o.iom.  (4  inches),  in  thickness,  well  rammed,  or 
better  still,  compressed  with  grooved  rollers.  More- 
over, it  must  be  protected  on  the  side  of  the  water  by 
means  of  some  sort  of  stone  work  to  prevent  the 
waves  from  injuring  the  slopes  of  the  dam.  Whence 
it  follows  that,  in  spite  of  the  coarseness  of  the  mater- 
ials used,  earthen  dams  cannot  but  be  costly. 

In  respect  to  economy  they  do  not  therefore  offer 
any  special  advantages  over  masonry  walls. 

If  we  compare  earthen  dams  sustaining  a  pond  30 
metres  (100  feet)  deep  with  masonry  walls  of  the 
same  height,  we  find  that  the  wall  requires  332  cubic 
metres  of  masonry  per  running  metre  (132  cubic  yards 
per  running  foot),  which  at  $4.00  per  cubic  metre 
for  everything,  including  the  facing,  gives  $1,328. 

With  its  slopes  of  i  perpendicular  to  2  base,  its 
crown  set  at  3  metres  (10  feet)  above  the  level  of  the 
water,  and  with  a  dry  stone  paving  on  the  up-stream 
side,  the  earthen  dam  would  cost  per  running  metre  : 

3062  cubic  yards  of  embankment  @  $0.37 $1133.05 

96.46     "        "      "  dry  stone  pavement  @  $0.75  .  .  .  $72. 34 


Total $1,205.39 

which  is  very  nearly  the  same  price  as  the  wall.     The 
difference  even  disappears  if  we  consider  the  interest 


STUDY    ON    RESERVOIR   WALLS.  25 

on  the  capital  engaged  during  construction  and  the 
long  repairs  that  are  sometimes  required  by  large  em- 
bankments on  account  of  the  settling  of  the  earth. 

Viewing  the  question  from  all  sides,  it  seems  to  me 
that  there  is  a  real  advantage  in  building  reservoir 
dams  of  masonry,  whenever  the  ground  shows,  at  a 
reasonable  depth,  sufficiently  firm  strata  on  which  to 
build,  and  it  is  only  when  proper  bottom  cannot  be 
found  that  recourse  should  be  had  to  earthen  dams. 

It  seems  to  me,  then,  that  masonry  dams  should  be 
the  rule  and  the  Bothers  the  exception,  especially  for 
great  heights. 

Kind  of  masonry  to  be  used. — The  dimensions  and 
shapes  for  the  walls  of  reservoirs  depend,  it  can  easily 
be  understood,  on  the  strength  of  the  material  used.  It 
is  therefore  interesting  to  examine  what  kinds  of 
masonry  should  be  put  into  them. 

The  Spanish  engineers,  in  these  sorts  of  structures, 
as  well  as  in  the  others,  used  immense  amounts  of  cut 
stone.  This  choice  seems  to  have  been  brought  about 
by  the  abundance  of  quarries  over  a  great  part  of 
their  territory,  and  also  by  certain  habits  of  size  and 
majesty  inherent  in  their  character. 

The  French  engineers,  yielding  to  other  considera- 
tions and  following  other  customs,  have,  especially  in 
later  times,  used  more  common  materials.  Which 
were  right,  the  French  or  the  Spanish  ?  This  is  what 
we  must  examine. 


26  STUDY    ON    RESERVOIR   WALLS. 

Under  ordinary  circumstances,  masonry  of  rough 
random  stone,  set  firmly  in  good  hydraulic  mortar, 
does  not  cost,  all  facing  included,  more  than  $4  per 
cubic  metre  ($3.05  per  cubic  yard).  Cut  stone  as  a 
general  rule  costs  three  or  four  times  as  much  and 
can  sustain  but  little  more  than  double  the  load. 
Whence  it  follows  that  it  is  better,  as  regards  economy, 
to  make  a  surface  of  a  given  strength  with  rough 
masonry  rather  than  with  cut-stone. 

In  the  present  case  the  preference  has  also  another 
cause.  The  external  forces  that  a  reservoir  wall  re- 
sists have  directions  which  depend  upon  the  shape  of 
the  inner  face  and  which,  as  a  rule,  are  but  slightly  in- 
clined to  the  horizon.  Hence  it  is  necessary  to  give  a 
certain  width  to  the  base,  otherwise  the  resultant  of 
the  thrusts  and  pressures  might  pass  outside.  It  is 
therefore  evident  that  if  we  wished,  in  order  to  reduce 
the  width  of  the  base,  to  utilize  the  full  strength  of 
the  stone,  it  could  only  be  done  within  very  narrow 
limits,  which  would  not  by  any  means  make  up  the 
difference  in  the  cost  of  the  materials. 

For  economical  reasons  as  well  as  for  facility  in 
building,  it  seems  to  me  certain  that  rubble  masonry 
is  what  should  be  used.  The  joints  should  be  irregu- 
lar on  the  faces  and  in  all  the  sections ;  the  courses 
should  be  thoroughly  inter-locked,  or  better  still  there 
should  be  no  courses,  and  by  means  of  good  work  this 
result  must  be  obtained,  so  that  the  whole  body  of  the 
wall  shall  be  a  real  monolith. 


STUDY    ON    RESERVOIR   WALLS.  2J 

Rubble  masonry  has  also  this  advantage  that  it 
adapts  itself  without  any  special  stones  to  every  possi- 
ble sort  of  shape.  The  most  complex  curves  require  no 
other  care  than  to  define  them  by  means  of  suitably 
placed  templets  on  which  the  mason  directs  his  work. 
This  advantage  is  also  not  to  be  overlooked. 

Weight  of  a  cubic  yard  of  masonry. — -The  weight 
of  a  cubic  yard  of  well-built  masonry  of  hard  stone, 
granite  or  limestone,  may  be  set  at  3,900  pounds  and 
is  thus  determined  : 

For  an  actual  volume  of  0.67  of  stone  at  4,250 

pounds  per  cubic  yard , . .  2,847  Ibs. 

For  an  actual  volume  of  0.33  of  mortar  at  3,230 
pounds  per  cubic  yard J,o77  Ibs. 


which  makes  in  all 3,924  Ibs. 

Or  in  round  numbers  3,900  pounds  (2,300  kilograms 
per  cubic  metre). 

By  adopting  almost  everywhere  the  figure  of  3,400 
pounds  (2,000  kilograms  per  cubic  metre),  more 
convenient  it  is  true  in  calculations,  engineers  seem 
to  me  to  have  unduly  lightened  the  true  weight  of  the 
structure. 

Limit  of  the  strain  to  be  put  upon  the  masonry. — It 
being  granted  that  reservoir  walls  should  be  built  of 
hard  rubble  masonry,  well  made  with  hydraulic  mortar, 
I  think  that  they  should  never  be  called  upon  to  sus- 
tain a  greater  strain  than  6  kilograms  per  square 
centimetre  (85  pounds  per  square  inch). 


28  STUDY    ON    RESERVOIR   WALLS. 

Certainly,  under  ordinary  circumstances,  well  built 
masonry  of  this  kind  should  sustain  a  much  greater 
weight. 

But  we  must  remark  that  the  formulae  by  means  of 
which  we  determine  the  decomposition  and  transmis- 
sion of  the  forces  acting  on  large  reservoir  walls,  are 
only  founded  on  hypotheses  which  it  is  impossible  to 
verify  exactly.  Hence  we  obtain  probable  results,  but 
absolute  certainty  is  wanting,  and  consequently  we 
must  be  prudent. 

And,  as  a  matter  of  fact,  the  upper  parts  of  dams 
must  resist  the  action  of  waves  and  ice,  and  may,  in 
heavy  squalls,  receive  violent  shocks.  On  the  other 
hand,  there  may  be  added  to  the  pressure  of  the  water 
at  the  lower  part,  the  pressure  of  a  thick  deposit  of 
mud,  which  greatly  increases  the  transverse  strains. 
These  circumstances  must  be  taken  into  consideration. 

If,  by  adopting  a  maximum  resistance  of  8  kilo- 
grams per  square  centimetre  (115  pounds  per  square 
inch)  instead  of  6,  the  volume  of  the  masonry  used 
would  be  reduced  in  proportion  of  6  to  8,  the  interest 
attaching  to  a  complete  utilization  of  the  strength 
of  the  masonry  might  be  understood ;  but  such 
is  not  the  case.  For  such  an  overcharge  the  sav- 
ing in  volume  is  not  much,  and,  when  everything  is 
taken  into  account,  we  should  be  exposed,  without 
special  advantages,  to  very  great  risk. 

For  it  must  always  be  borne  in  mind  that  of  all 
hydraulic  structures,  the  reservoir  wall  is  perhaps  the 


STUDY    ON    RESERVOIR   WALLS.  29 

most  difficult  to  properly  repair  after  it  has  once  been 
seriously  damaged.  It  is  also  the  one  which  causes 
the  most  disastrous  consequences  if  once  it  gives  way. 

The  breaking  of  the  Puentes  dam  on  the  3oth  of 
April,  1 802,  caused  the  loss  of  608  persons  and  destroyed 
the  little  town  of  Lorea  containing  809  houses. 

The  rupture  of  the  Sheffield  dam  also  caused  the 
deaths  of  many  persons  and  the  ruins  of  many  struct- 
ures. 

In  view  of  such  chances,  the  engineer  must  not  be 
too  bold,  nor  take  upon  himself,  before  the  public,  a 
responsibility  which  is  powerless  to  repair  such  disas- 
ters. 

However  little  it  may  lean  toward  rashness,  bold- 
ness, in  such  a  case,  may  become  almost  a  crime.  It 
should  be  severely  proscribed  and  the  rule  of  strict 
prudence  should  always  be  followed.  In  my  opinion, 
it  is  better  not  to  build  reservoir  walls  if  we  have  not 
the  necessary  resources  to  build  solidly,  than  to  build 
carelessly  and  at  the  risk  of  frightful  catastrophes. 

On  all  these  accounts  I  think  that  in  calculating 
strength,  the  pressure  of  6  kilograms  per  square  cen- 
timetre (85  pounds  per  square  inch)  should  never  be 
overstepped. 

Considerations  on  the  shape  to  be  given  to  reservoir 
walls. — I  have  said  before  that  rubble  masonry  is  bet- 
ter than  any  other  for  building  reservoir  walls,  because 
with  it  we  can  follow  any  shape  without  having  the 


30  STUDY    ON    RESERVOIR   WALLS. 

trouble  of  cutting  any  special  stones,  and  consequently 
we  are  left  free  to  choose  that  shape  of  profile  which 
will  offer  the  greatest  amount  of  strength. 

I  have  also  said  that  it  is  prudent  not  to  exceed  a 
pressure  of  6  kilograms  per  square  centimetre  (85 
pounds  per  square  inch)  of  surface,  and  finally  that  we 
are  about  right  in  taking  the  weight  of  the  masonry  at 
2,300  kilograms  per  cubic  metre  (3,900  pounds  per 
cubic  yard). 

This  granted,  the  data  essential  to  determining  the 
shape  of  the  profile  are  given  and  we  can  proceed  to 
the  calculations.  Still  it  is  not  uninteresting  to  exam- 
ine another  accessory  arrangement,  very  frequently 
adopted  in  Spain  but  generally  neglected  in  France. 
I  mean  the  shape  of  the  wall,  curved  in  plan  with  its 
convex  side  up-stream.  At  the  first  glance  we  see 
that  this  curve  must  transfer  a  part  of  the  pressures 
to  the  sides  of  the  valley,  and  that  the  wall,  under  the 
action  of  the  heads  of  water,  closing  tighter  against  the 
solid  banks  that  hold  it,  has  no  tendency  to  turn  over. 
A  short  but  sufficiently  accurate  calculation  shows 
this  first  impression  to  be  right. 

If,  in  a  curved  reservoir  wall,  we  take  a  horizontal 
section  at  a  depth  h  below  the  level  of  the  water,  if  we 
call  e  the  uniform  thickness  of  the  wall  of 
the  section  under  consideration,  R  the  mean 
radius  of  curvature,  w  the  weight  of  the 
unit  of  the  liquid  and  w  the  mean  load  on 
the  thickness  e,  we  may,  with  a  certain  de- 


STUDY    ON    RESERVOIR   WALLS.  31 

gree  of  exactness,  establish  the  following  relation  be- 
tween these  different  quantities : 

w  h  R  =  w  e. 

If  we  now  make  w=  1,000  kilograms  per  cubic 
metre  (62.5  pounds  per  cubic  foot),  w'  =  60,000  kilo- 
grams per  square  metre  (12,240  pounds  per  square 
foot),  e  =  %  h,  we  shall  find  R  —  20  metres  (65  feet.) 

Which  means  that  under  the  above  conditions  we 
may,  by  laying  out  the  wall  on  a  curve  of  20  metres 
(65  feet)  radius,  transfer  the  pressure  of  the  water  to 
the  sides  of  the  valley,  which  will  thus  act  as  abutments, 
and  that,  too,  no  matter  what  the  height.  But,  on  the 
other  hand,  this  arrangement  in  a  curve  does  not  at  all 
lessen  the  effect  of  the  weight  of  the  masonry,  which, 
acting  perpendicularly  to  the  plane  of  the  section  con- 
sidered, cannot  be  transmitted  to  the  end.  Hence  it 
fqllows  that  whether  the  structure  be  curved  or  not, 
its  weight  must  always  be  supported  in  the  same  way. 
The  saving  that  follows  the  adoption  of  a  curved  shape 
has  a  bearing  only  on  the  increase  that  must  be  given 
to  a  wall  which  already  supports  its  own  weight,  in 
order  to  make  it  support,  at  the  same  time,  the  press- 
ure of  the  Water. 

This  reduces  by  a  large  amount  the  profit  derived 
from  adopting  a  curved  form ;  still,  though  thus  lim- 
ited, the  advantage  is  real,  and  we  cannot  afford  to 
set  it  aside  wherever  the  locality  will  allow  its  use. 
But  it  will  be  prudent  not  to  consider  it  in  making  our 


32  STUDY    ON    RESERVOIR    WALLS. 

calculations  for  stability.     The  result  of  this  voluntary 

omission  will  be  to  obtain  in  the  structure  an  excess 

• 

of  strength  which  is  never  to  be  despised. 

In  France  and  elsewhere,  reservoir  walls  have  'fre- 
quently been  reinforced  by  means  of  counterforts. 
The  usefulness  of  this  device  is,  in  my  opinion,  very 
doubtful.  If  the  wall  is  strong  enough  by  itself,  it  is 
clear  that  the  counterforts  are  a  useless  expense  as 
well  as  a  complication  in  the  system  of  construction. 

If  the  wall  is  not  sufficiently  strong,  the  counterforts 
will  not  prevent  it  from  yielding  under  the  pressure  as 
may  be  seen  in  the  Lampy  and  Grosbois  reservoirs. 

In  a  word,  the  masonry  intended  for  the  counterforts 
will  always  be  better  used  if  it  be  spread  over  the 
wall  than  if  it  be  used  by  itself  under  the  shape  of 
pillars  or  projecting  masses. 

This  being  said,  counterforts  suppressed,  curvature 
admitted  as  an  excess  of  strength,  what  should  be  the 
profile  of  the  wall  ? 

In  order  to  determine  it,  we  need  consider  but  one 
element  of  the  wall  included  between  two  adjacent 
vertical  'planes  perpendicular  to  the  face  of  the  wall, 
then  arrange  it  so  that  it  will  resist  by  itself  the  loads 
and  pressures  put  upon  it.  And  in  fact, 'it  is  clear 
that  if  each  of  these  elements,  taken  by  itself,  be 
sufficiently  strong,  its  connection  with  the  adjoining 
elements  and  with  the  sides  of  the  valley  can  only  in- 
crease the  stability  of  the  whole. 

The  question  then  resolves  itself  into  making  one 


STUDY    ON    RESERVOIR    WALLS.  33 

element  stable,  and  for  this  two  situations  are  to  be 
considered,  which  are  the  extreme  terms  of  the  suc- 
cessive situations  through  which  the  wall  passes,  when 
the  reservoir  being  empty  it  is  filled  to  its  highest 
point,  or  being  entirely  full  it  is  reduced  to  complete 
emptiness.  In  a  word,  the  wall  must  be  wholly  stable 
before  the  pond  exists  and  after  it  is  complete.  Sta- 
bility, being  established  for  these  two  extreme  cases, 
must  exist  in  all  the  intermediate  positions,  about 
which  we  need  give  ourselves  no  concern. 

When  the  reservoir  is  empty,  the  wall  only  supports 
its  own  weight,  but  even  then  the  base  carries  a  heavy' 
load.  Thus  it  is  easy  to  see  that  if  the  wall  has  a 
uniform  thickness,  it  cannot  be  more  than  26  metres 
(85.3  feet)  high  before  the  pressure  on  the  base  ex- 
ceeds 6  kilograms  per  square  centimetre  (85  pounds 
per  square  inch).  If  the  faces  be  inclined  so  as  to 
reduce  the  mean  thickness  to  one-half  and  then  to  one- 
third  of  the  width  of  the  base,  the  height  compatible 
with  a  pressure  of  6  kilograms  rises  to  52  metres 
(170.6  feet),  then  to  78  metres  (255.9  feet). 

This  simple  consideration  shows  that  it  is  absolutely 
necessary  to  widen  the  base  of  the  walls  by  inclining 
the  up  and  down-stream  faces.  If  the  wall  were  not 
exposed  to  a  heavy  pressure  on  its  up-stream  face  the 
batirs  on  the  two  faces  would  be  the  same,  and,  by  this 
fact  of  complete  symmetry,  the  pressures  would  be 
uniformly  distributed. 

But  when  the  water  is  in  and  the  reservoir  is  full, 

3 


34  STUDY   ON    RESERVOIR  WALLS. 

the  water  bears  upon  the  up-stream  face  of  the  wall 
and  there  develops  a  pressure  which  increases  with  the 
square  of  the  depth  of  the  water.  In  deep  reservoirs 
this  pressure  becomes  enormous.  Made  up  of  ele- 
ments normal  to  the  face  of  the  wall,  it  exerts  its  final 
effect  in  a  nearly  horizontal  direction  and  carries  the 
maximum  load  to  the  back  of  the  wall.  The  weight, 
however,  not  ceasing  to  act,  these  two  forces  have  a 
resultant  which  must,  for  stability,  pierce  the  base  in 
front  of  the  back  edge.  Hence  arises  the  necessity  of 
giving  to  the  down-stream  face  a  greater  batir  than  to 
the  up-stream. 

I  have  taken  for  the  up-stream  batir  the  fixed  ratio 
of  five  perpendicular  to  one  base.  For  the  down- 
stream face  the  ratio  is  not  fixed  but  increases  with  the 
height.  To  justify  this  arrangement  it  will  be  suffi- 
cient to  turn  to  tables  \\a  and  lid,  and  see  that  the 
pressures  increase  regularly  and  that  they  nowhere 
exceed  the  limits  adopted. 

To  sum  up,  the  wall  of  a  reservoir  must  have  some- 
what the  same  silhouette  as  a  wrestler  who  is  ready  to 
receive  a  shock,  and  who,  well  set  on  his  legs,  has  car- 
ried one  a  little  forward  while  the  other  is  strongly 
planted  behind. 

Width  at  the  top. — Theoretically  the  width  of  the 
wall  at  the  top  might  be  nothing,  since  at  this  point 
there  is  neither  a  pressure  of  water,  nor  any  weight  of 
masonry.  But  in  practice  we  must  consider  the  shock 


STUDY    ON    RESERVOIR   WALLS.  35 

of  waves  and  ice  which  may,  in  certain  cases,  acquire 
great  strength  and  exert  a  powerful  destroying  action 
at  the  top. 

The  wall  also  should  be  made  use  of  to  form  a 
means  of  communication  between  the  two  slopes  of 
the  valley.  The  interest  in  thus  using  the  wall  as  a 
viaduct  is  the  greater  in  proportion  as  the  pond  is 
deeper,  and,  consequently,  as  the  lake  artificially 
formed  extends  further  and  forms  a  greater  obstacle 
to  communication. 

Without  having  any  absolute  connection  with  the 
depth  of  the  pond,  the  width  of  the  crown  depends 
upon  it  to  a  certain  extent,  and  we  easily  see  that  it 
must  increase  at  the  same  time.  It  seems  to  me 
scarcely  possible  to  reduce  it  below  2  metres  (6.56 
feet)  for  small  ponds,  nor  necessary  to  make  it  more 
than  5  metres  (16.40  feet)  for  the  largest.  I  think  it 
should  be  kept  within  these  limits. 

Height  of  the  crown. — M.  Minard  mentions,  in  his 
Cours  de  construction,  waves  which  rose  3  metres  (9.84 
feet)  above  the  water  level  in  the  Chazilly  reservoir, 
the  pond  being  but  1,500  metres  (4,900  feet)  long 
and  20  metres  (66  feet)  deep. 

Waves  have  reached  the  height  of  2  metres  (6.56 
feet)  in  the  Cercey  reservoir,  the  greatest  length  of 
which  is  900  metres  (2,950  feet),  and  depth  10  metres 
(33  feet). 

The  size   of    waves  depends  upon  very  complex 


36  STUDY    ON    RESERVOIR   WALLS. 

causes,  among  which  may  be  mentioned  the  force  and 
direction  of  the  wind,  the  length  of  the  pond  and  the 
depth  of  the  water ;  but  it  is  difficult,  if  not  impos- 
sible, to  establish  any  exact  relation  between  the  phe- 
nomenon and  its  different  causes — in  other  words,  to 
fix  in  advance  the  height  that  the  waves  will  reach  in 
any  given  case. 

Having  a  certain  number  of  observations  as  a  basis, 
I  think  that  the  height  of  the  crown  should  increase 
with  the  depth  of  the  water,  and  I  have  set  3.50 
metres  (11.50  feet)  as  a  maximum,  not  including  the 
parapet.  Still,  if  there  were  any  occasion  for  chang- 
ing the  figures  given  in  column  4,  tables  la  and  Ib,  it 
should  be,  in  my  opinion,  rather  by  increasing  than  di- 
minishing them.  In  fact,  it  is  hard  to  see  that  there 
would  be  any  serious  disadvantage  in  having  the  crown 
a  metre  (3.28  feet)  too  high.  But  there  would  be  a 
great  inconvenience  in  having  it  a  metre  too  low, 
especially  were  the  wall  to  be  used  as  a  viaduct. 

Justification  of  the  types. — The  object  of  the  pre- 
ceding considerations  is  to  state  the  problem  dis- 
tinctly, and  to  clearly  define  the  conditions  that  the 
wall  must  fulfill. 

This  done,  in  order  to  find  the  solution,  we  only 
have  to  resort  to  the  strict  formulae  of  analysis,  and 
to  establish  an  exact  connection  between  the  various 
variables,  of  which  the  relations  have  been  pointed  out 
in  a  general  way.  But,  on  this  point,  I  can  do  neither 


STUDY    ON    RESERVOIR    WALLS.  37 

better  nor  more  than  those  who  have  gone  before  me, 
nor  can  I  say  anything  that  has  not  already  been  set 
forth  with  so  much  authority  by  Sazilly  first  and  after- 
wards by  Delocre  (and  again  by  Pelletreau.  Tr.)  For 
the  theoretical  study  of  the  subject  I  shall  therefore 
limit  myself  to  referring  to  the  excellent  articles  which 
I  have  mentioned,  and  approaching  the  problem  by 
another  road,  I  shall  justify,  a  posteriori,  my  profile- 
type  by  showing  that  it  fulfills  in  all  respects  the 
various  conditions  that  we  have  sought  to  obtain. 

Sliding  on  the,  base  or  on  the  courses. — A  reservoir 
wall  is  necessarily  founded  on  a  bed  of  firm  rock. 
The  defective  parts  must  be  cleared  away,  and  the 
rock  cut  into  steps  rising  from  the  up-  to  the  down- 
stream side,  or,  more  simply  still,  irregularly  cut 
down,  with  projections  left  here  and  there  in  the 
sound  parts  of  the  mass. 

I  have  said  before  that  the  masonry  should  be 
rubble,  without  any  regular  beds,  so  built  as  to  form 
a  true  monolith. 

Under  these  conditions  sliding  is  impossible,  either 
of  the  wall  on  its  foundation,  or  of  one  bed  on  an- 
other. 

Still,  it  is  not  uninteresting  to  inquire  what  would 
happen  to  the  proposed  profile,  if  these  precautions 
were  not  taken. 

Now,  we  know  that  the  force  required  to  make  two 
pieces  of  cut  stone  slide  upon  each  other,  when  both 


38  STUDY    ON    RESERVOIR   WALLS. 

are  dry,  or  when  they  are  joined  by  fresh  mortar,  is 
equal  to  about  o.  75  of  the  normal  pressure.  Whence 
it  follows  that  the  sliding  of  our  walls  would  only  be 
possible  when  the  horizontal  thrust  reached  three- 
fourths  of  the  sum  of  the  vertical  pressures.  If  we 
consult  line  17,  of  tables  \\a  and  \\b,  we  find  that  the 
ratio  of  the  thrust  to  the  pressure  varies  from  0.34 
to  0.51. 

With  these  conditions,  and  even  more  so  when  the 
foundation  bed  shall  have  been  cut  down  with  the 
care  that  should  be  taken  to  make  it  rough  and  lumpy, 
there  would  be  no  tendency  to  slide. 

Tendency  to  overturn. — Made  with  good  hydraulic 
mortar,  masonry  has  a  great  deal  of  cohesion  and  ad- 
heres strongly  to  the  rock,  whence  it  follows  that  it 
can  resist  the  considerable  forces  of  traction,  which 
should  be  considered  in  calculating  the  resistance 
against  overturning.  But,  to  simplify  the  problem,  I 
shall  suppose  that  the  wall  does  not  adhere  to  its  bed, 
and  that  the  condition  to  be  fulfilled  to  prevent  over- 
turning is,  that  the  moment  of  the  thrust  shall  be  less 
than  the  moment  of  the  vertical  pressures,  distances 
being  measured  with  regard  to  the  down-stream  edge. 
Now,  line  16,  tables  Ha  and  lib,  shows  us  that  the 
ratio  between  these  two  moments  varies  from  0.19  to 
0.40.  Hence  there  is  perfect  stability  in  this  respect, 
without  even  considering  the  force  of  cohesion,  which 
is  still  real. 


STUDY    ON    RESERVOIR   WALLS.  39 

Pressures  on  the  base. — When  the  resultant  of  the 
pressures  pierces  the  base  at  an  equal  distance  from 
the  two  outside  edges,  there  is  no  reason  why  these 
two  edges  should  be  unequally  loaded.  We  assume, 
and  we  must  assume,  that  they  are  equally  so.  But 
if  the  resultant  approach  one  edge  the  equality 
ceases,  and  the  nearer  edge  to  the  point  of  appli- 
cation of  the  resultant  supports  a  greater  share  of  the 
load.  I  have  adopted  for  the  determination  of  the 
pressures  the  following  usual  rule  : 

/  being  the  width  of  the  wall,  R  the  resultant  of 
the  pressures,  u  the  distance  of  the  point  of  applica- 
tion of  this  resultant  from  the  nearer  edge,  and  P  the 
maximum  pressure,  we  have 

27?  2R   ( 

P= ;or/>  =  — 7-1   2—  V 

3  u*  I    \          I 

according  as  u  is  less  or  greater  than  — • 

o 

This  granted,  when  the  pool  is  empty,  all  the  forces 
are  summed  up  in  a  weight  which  is  nearer  the  front 
edge  than  the  other ;  hence  it  is  on  the  front  edge 
that  the  maximum  pressure  is  found.  Calculated 
according  to  the  preceding  rule,  it  never  exceeds  5.97* 
say  6  kilograms  per  square  centimetre  (85  pounds 
per  square  inch). 

The  average  pressure,  supposing  it  to  be  uniformly 
distributed  over  the  entire  base,  nowhere  exceeds  4.55 
kilograms  (64. 70  pounds). 


40  STUDY    ON    RESERVOIR   WALLS. 

The  ratio  of  the  second  to  the  first  never  falls  be- 
low 0.62,  which  shows  a  good  distribution  of  the  forces. 

When  the  pool  is  full,  the  resultant  of  the  forces 
is  no  longer  vertical.  If  it  be  decomposed  at  its 
point  of  application  into  two  components,  one  parallel 
and  the  other  normal  to  the  base,  we  find  that  the 
horizontal  component,  which  is  but  the  thrust  of  the 
water  on  the  vertical  projection  of  the  wall,  is  power- 
less to  cause  any  sliding  on  the  base.  Moreover, 
on  account  of  its  direction,  it  does  not  aid  in  in- 
creasing the  load  which  remains  due  to  the  ver- 
tical component.  The  point  of  application  of  the 
resultant  being  nearer  to  the  down-stream  edge  than 
to  the  other,  it  is  the  down-stream  edge  that  sustains 
the  maximum  pressure.  In  no  type  does  it  exceed 
5.71  kilograms  per  square  centimetre  (81.20  pounds 
per  square  inch).  Uniformly  distributed  it  reaches 
5.65  kilograms  (80.24  pounds). 

The  ratio  of  the  mean  to  the  maximum  pressure 
varies  from  0.50  to  0.98.  But  for  the  great  heights  it 
approaches  unity,  a  result  we  should  try  to  obtain. 

Expenses  compared. — In  what  precedes  I  have  tried 
to  show  that  the  types  are  sound,  so  far  as  stability  is 
concerned.  I  have  shown  that  they  are  secure  against 
sliding,  overturning,  and,  finally,  whether  the  pond  be 
full  or  empty,  there  is  no  load  on  them  which  at  any 
point  exceeds  6  kilograms  per  square  centimetre  (85 
pounds  per  square  inch). 


STUDY    ON    RESERVOIR   WALLS.  41 

Undoubtedly,  when  we  think  on  the  one  hand  of 
the  difficulty  of  making  extensive  repairs  in  reservoir 
walls,  and  on  the  other  of  the  frightful  disasters  which 
their  giving  way  may  involve,  we  are  led  to  consider 
perfect  stability  as  the  first  condition  to  be  fulfilled. 
This  goes  far  beyond  all  the  others,  and  there  must 
be  no  doubt  whatever  as  to  the  solidity  of  the  wall. 

But  this  condition  being  fulfilled,  we  may  examine 
the  question  of  cost,  because  these  kinds  of  works, 
always  very  expensive,  may,  if  they  be  badly  de- 
signed, cause  the  locking  up  of  a  great  deal  of  cap- 
ital. We  must  therefore  examine,  on  the  score  of 
economy,  the  value  of  the  types  which  I  offer. 

The  best  means  of  justifying  these  types  is  to  com- 
pare them  with  already  existing  similar  works. 

This  comparison  has  no  bearing  except  on  the 
quantities  of  masonry  which  both  require,  because  we 
must  suppose  that  the  masonry  will  be  everywhere 
built  in  the  same  way,  and  always  very  simply. 

The  comparison  of  volumes  manifestly  becomes 
that  of  the  surfaces  of  sections,  and  consequently  can 
readily  be  made  clear  to  the  eye. 

In  figures  21,  22  and  following,  14  specimens  are 
thus  compared  with  the  types,  and  it  is  the  result  of 
this  comparison  which  I  am  about  to  examine. 

Walls  of  Spanish  reservoirs. — The  group  of  Span- 
ish walls  is  first  presented,  with  their  imposing  and 
useless  size  (figs.  22,  23,  24,  25,  28  and  29). 


42  STUDY    ON    RESERVOIR   WALLS. 

I  attach  so  high  an  importance  to  perfect  safety 
that  I  should  feel  very  indulgent  for  this  immoderate 
luxury  if,  in  doubling  the  volume  of  the  masonry, 
they  had  at  the  same  time  reduced  the  pressures  to 
a  large  extent.  Unfortunately,  not  this  but  the  re- 
verse is  the  case.  Thus,  for  example,  in  the  Elcho 
and  Alicante  dams  the  maximum  pressures  reach  12.70 
kilograms  and  11.30  kilograms  per  square  centimetre 
(200.59  Ibs.  and  160.69  Ibs.  per  square  inch)  respec- 
tively. It  is  nearly  the  same  thing  with  the  others. 

The  superiority  of  our  later  French  types,  so  sober 
and  so  correct,  over  the  cyclopean  types  of  the  Span- 
ish walls,  cannot  for  an  instant  be  doubted. 

Old  walls  of  French  reservoirs. — The  French  walls 
existing  before  Sazilly's  article  also  form  an  interest- 
ing class  to  examine.  This  is  the  object  of  figs.  30, 
31,  32,  33  and  34. 

I  n  these  there  is  no  longer  cause  for  reproach  in  the 
dangerous  luxury  of  masonry.  Still  there  is  consider- 
able but  at  the  same  time  much  less  excess. 

All  these  examples,  however,  contain  markedly  more 
masonry  than  the  new  types,  and  err  in  regard  to  econ- 
omy ;  but  this  is  not  the  strongest  reproach  which  a 
judicious  criticism  might  most  justly  cast  upon  them. 

By  examining  them  closely,  we  easily  see  the  uncer- 
tainty that  then  existed  in  the  minds  of  engineers  on 
the  nature  of  the  forces  to  be  overcome.  For  example, 
in  the  Gros-Bois  and  Glomel  walls  almost  all  the  sur- 


STUDY    ON    RESERVOIR   WALLS.  43 

plus  thickness  is  placed  on  the  up-stream  side.  The 
contrary  is  the  case  in  the  Bosmelea  wall. 

That  of  Vioreau  is  a  sort  of  rectangle  with  nearly 
vertical  faces.  At  Lampy,  the  projections  are  marked, 
but  they  are  about  equal  on  the  two  sides. 

All  the  profiles  are  incorrect,  and  the  very  diversities 
of  their  defects  clearly  show  the  absence  of  any  sound 
theory. 

New  French  walls. — The  group  of  new  French 
walls,  represented  by  those  of  the  Habra  (fig.  27),  of 
Ternay  (fig.  26)  and  of  the  Furens  (fig.  21),  appears 
with  an  air  of  close  relationship  and  an  undoubted 
superiority.  We  easily  see  that  they  proceed  from  the 
same  order  of  ideas  and  that  the  theory  of  walls  is 
made  and  accepted  by  engineers. 

Here  the  comparison  becomes  more  serious. 

WALL   OF   THE    HABRA. 

It  is  clear,  at  the  first  glance,  that  the  type  proposed 
requires  about  the  same  quantity  of  masonry  as  that 
of  the  Habra.  In  regard  to  economy  there  is  very- 
little  to  choose  between  them. 

But  the  superiority  from  this  point  of  view  would  be- 
long to  the  profile-type  if  that,  which  I  cannot  but 
regard  as  a  mistake  in  the  shape  of  the  parapet  of  the 
other,  were  corrected.  It  seems  to  me  certain  that  if 
the  wind  were  to  raise  waves  in  the  pond,  they  would 
pass  over  the  parapet,  and  might  even  upset  it.  This 


f     '  >v>>\l 

OTiyifcaTtf 


44  STUDY    ON    RESERVOIR   WALLS. 

is  a  fault  of  inadvertence  which  should  be  corrected, 
and  if  what  is  necessary  in  this  respect  be  done,  our 
profile-type  will  show  a  slight  saving  on  the  other. 

WALL    OF    TERNAY. 

The  profile- type,  as  may  be  seen  in  fig.  26,  has  a 
little  more  of  a  batir  up-stream  than  the  Ternay  wall. 
On  the  other  hand  it  has  a  little  less  masonry  down- 
stream. On  the  whole  the  two  balance  each  other. 

The  reservoir  wall  of  Ternay,  which  was  remarkably 
planned  and  built  by  M.  Bouvier,  has,  in  my  opinion, 
scarcely  a  defect.  The  up-stream  face  is  a  little  too 
stiff.  The  pressure  when  empty  is  thereby  increased 
and  certainly  exceeds  6  kilograms  per  square  centi- 
metre (85  pounds  per  square  inch). 

WALL    OF    THE    FURENS. 

The  reservoir  wall  of  the  Furens  is  to-day  the  great- 
est of  the  works  of  this  sort,  at  least  so  far  as  my 
knowledge  goes,  because  that  of  Puentes,on  account  of 
a  great  mistake  made  in  the  foundations,  was  partly 
destroyed  in  1802,  and  has  not  since  been  rebuilt. 

The  Furens  wall  reflects  the  greatest  honor  on 
Messrs.  Grseff,  Delocre  and  Montgolfier,  the  engineers, 
who  prepared  the  plans  and  carried  the  undertaking 
through  to  a  successful  termination. 

If  I  compare  my  profile  type  with  the  Furens  wall,  I 
find  to  the  disadvantage  of  the  former  an  excess  of 
volume  of  about  10  per  cent,  which  is  certainly  to  be 
considered. 


STUDY    ON    RESERVOIR   WALLS.  45 

I  might  say  that  the  designers  of  the  reservoir  wall 
profited  skillfully  by  the  narrowness  of  the  valley  to 
build  on  a  curve  and  to  narrow  the  base  of  their  found- 
ations. 

They  might  even  have  made  greater  reductions  had 
they  taken  full  advantage  of  these  facilities  of  which 
the  profile  type  makes  no  account.  All  this  is  correct ; 
but  it  is  not  the  essential  cause  of  the  difference  in  ques- 
tion. It  arises  mainly  from  their  having  taken  the 
weight  of  the  masonry  at  2,000  kilograms  per  cubic 
metre  (3,400  pounds  per  cubic  yard),  whereas  I  have 
taken  it  at  2,300  kilograms  (3,900  pounds).  What  I  saw 
at  the  Ternay  dam,  when  as  chief  engineer  I  directed 
its  construction,  leads  me  to  think  that  the  actual 
weight  of  granite  masonry,  the  joints  being  well 
filled  with  mortar  and  spauls,  is  not  less  than  2,300 
kilograms  (3,900  pounds).  The  consequences  of  this 
difference  are  easily  seen. 

This  change  alone  increases  the  weight  of  the  wall 
1 5  per  cent.  Where  there  was  before  a  pressure  of  6 
kilograms  per  square  centimetre  (85  pounds  per 
square  inch),  we  must  now  count  on  6  x  1.15  or  6.90 
kilograms  (98  pounds). 

Having  resolved,  for  the  reasons  before  given,  not 
to  exceed  the  limit  of  6  kilograms  (85  pounds),  I  have 
had  to  widen  the  base  of  the  wall.  From  this  arises 
the  difference  of  10  per  cent,  which  exists  between  the 
given  section  of  my  profile  and  that  of  the  Furens 
wall. 


46  STUDY    ON    RESERVOIR   WALLS. 

But  having  assumed  this  limit  of  6  kilograms  (85 
pounds)  we  see  that  the  profile-types  can  scarcely  be 
reduced — in  other  words,  that  they  are  sufficiently  eco- 
nomical. 

Various  details. — It  is  not  uninteresting  to  examine 
how  the  crown  of  the  walls  should  be  built.  I  have 
given  before  the  conditions  which  govern  its  height 
and  width.  I  add  that  the  shock  of  waves,  and  the 
occasional  presence  of  ice,  should  cause  all  mouldings, 
steps,  projections  or  hollows  at  the  top  of  the  crown 
to  be  suppressed.  The  parapet  itself  should,  in  my 
opinion,  be  formed  only  of  a  solid  wall  smoothly 
rounded  at  the  top. 

The  ornamentation  of  the  wall  of  a  high  dam  is  only 
possible  on  the  down-stream  side  and  offers  a  few  dif- 
ficulties. I  think  that  it  must  be  limited  to  a  sort  of 
inverted  festoons,  supporting  an  open  work  parapet 
either  on  cut-stone  corbels  or  on  brick  ogives.  This 
is  the  only  system  of  decoration  which,  in  my  opinion, 
suits  such  works.  I  have  given  in  figures  12,  15,  18, 
three  specimens  for  various  heights. 

It  seems  proper  to  place,  on  the  face  next  the  water, 
iron  ladders,  by  means  of  which  persons  who  happen 
to  fall  into  the  water  can  climb  out  along  the  wall. 
Rings  should  also  be  put  in,  to  which  the  service  boats 
can  be  made  fast. 

On  the  down-stream  face,  cut-stone  corbels,  arranged 
in  quincunx  order,  will  allow  small  scaffolds  to  be 


STUDY    ON    RESERVOIR   WALLS.  47 

placed,  and,  if  necessary,  the  face  of  the  wall  can  be  vis- 
ited and  repaired. 


GENERAL  OBSERVATIONS. 

At  the  beginning  of  the  present  note  I  mentioned 
cursorily  the  services  which  husbanding  water  may 
render  to  agriculture,  to  manufacturers,  and  to  the 
health  of  cities. 

I  might  also  add  that  our  inland  navigation  receives 
its  share  of  the  benefits,  sometimes  in  the  supply  of 
water  for  canals  and  again  in  regulating  the  discharge 
of  rivers. 

The  essential  instrument  for  this  case,  which  consists 
in  storing  up  the  surplus  of  the  winter's  rains  for  use 
in  summer,  is  the  reservoir. 

Placed  necessarily  in  the  upper  parts  of  valleys,  the 
reservoir  presents  no  other  difficulties  nor  essential 
expense  than  the  building  of  the  dam. 

Earthen  embankments  or  masonry  walls  may  be 
used  in  forming  these  dams.  The  wall,  however,  es- 
pecially in  the  South,  is  to  be  preferred. 

It  is  certain  that  when  the  railway  system  shall  have 
been  finished,  attention  will  be  given  to  navigation  and 
to  storing  water.  Then  works  of  this  sort  will  become 
as  common  as  to-day  they  are  rare. 

Often  they  will  form  a  good  investment  for  capital, 
and  private  industry  will  be  interested  in  them,  in  or- 
der to  sell  the  stored-up  water. 


48  STUDY    ON    RESERVOIR   WALLS. 

The  establishment  of  a  reservoir  will  almost  always 
be  of  a  generally  useful  character  to  which  the  State 
cannot  be  indifferent  and  which  will  call  for  its  assis- 
tance. 

Counties  and  parishes  will  often  have  a  more  direct 
interest  in  these  kinds  of  works,  and  should  contribute 
to  them. 

Finally,  manufacturers  and  agriculturists  who  derive 
any  benefit  from  the  water  should  be  expected  to  pay 
for  the  good  they  receive. 

It  is  in  this  way,  coming  from  different  sources,  that 
the  funds  for  building  reservoirs  will  be  obtained. 

So  soon  as  private  parties  take  the  matter  up,  the 
question  of  economy  necessarily  occupies  a  foremost 
place.  Manufacturers  and  agriculturists,  who  cannot 
obtain  their  funds  by  means  of  the  easy  way  of  taxa- 
tion, are  obliged  to  count  with  their  purse  and  to  pay 
no  more  for  a  service  than  it  is  actually  worth  to  them. 

This  consideration  obliges  the  engineer  to  study  the 
matter  of  jcost  very  closely,  and  to  solve  it  in  the  best 
way  for  all  the  interests  concerned. 

A  district  needs  a  reservoir  of  a  given  capacity,  an 
examination  of  the  .sites  easily  shows  the  depth  of 
water  required  to  obtain  the  wished  for  amount.  This 
depth  found,  the  dimensions  and  price  of  the  dam  are 
deduced,  and  consequently  the  cost  of  the  water  stored 
up. 

This  is  probably  the  shape  in  which  the  problem 
will  generally  be  presented  to  the  engineer. 


STUDY    ON    RESERVOIR   WALLS.  49 

But  it  will  also  frequently  happen  that  a  minimum 
of  volume  being  fixed,  we  may  wish  to  know  what  it 
would  cost  to  increase  this  minimum,  and  at  what 
limit  the  increase  in  the  volume  stored  up  would  cease 
to  be  advantageous. 

These  questions,  in  order  to  be  properly  solved,  re- 
quire the  quick  preparation  of  plans.  The  engineer 
must  study  all  the  combinations  which  present  them- 
selves, promptly  and  with  sufficient  exactness. 

It  was  in  view  of  this  rapid  study  that  I  formerly 
prepared  the  present  article  for  my  own  service.  It 
is  still  in  view  of  this  study  that  I  now  offer  it  to  con- 
structors. 


SUMMARY 

OF   THE   PLATES   OF   THE   TYPES  OF   RESERVOIR   WALLS. 

Fig.  i.  Profile  type  of  reservoir  walls. 

"  2.  Type  for  height  of    5  metres,  16.40  feet. 

"  3.  "  "         10       "  32.81    " 

"  4-  "  (l         15       "  49-21    " 

"          5.  "  "  20         "  65.62      " 

6.  "  "        25  "          82.02    " 

"       7.  "  "        30  "          98.43    " 

8.  "  "        35  "         114.83    " 

"       9.  "  "        40  "         131.24    " 

"     10.  "  "        45  "         147.64    " 

"  '  ii.  "  "         50  "         164.04    " 

Figs.  12,  13,  14.   Type  of  crown  applicable  to  wallsrup  to  15  me- 
tres (49.21  feet)  in  height. 

Elevation. — Cross  section. —  Wall  10  metres  (32.81  feet)  in  height 
seen  from  down  stream. 
4 


SO  SUMMARY. 

Figs.  15,  1 6,  17.  Type  of  crown  applicable  to  walls  from  15  to  30 
metres  (49.21  to  9843  feet)  in  height. 

Elevation. — Cross  section. —  Wall  25  metres  (82.02  feet)  in  height, 
seen  from  down  stream. 

Figs.  1 8,  19,  20.  Type  of  crown  applicable  to  walls  from  30  to  50 
metres  (98.43  to  164.04  feet)  in  height. 

Elevation. — Cross  section. —  Watt  40  metres  (131.24  feet)  in  height, 
seen  from  down  stream. 

Fig.  21.  Graphic  comparison  of  the  profile  type  with  the  Furens 
Dam,  (France). 

Fig.  22.  Graphic  comparison  of  the  profile  type  with  the 
Puentes  Dam,  (Spain). 

Fig.  23.  Graphic  comparison  of  the  profile  type  with  the  Val 
de  Infierno  Dam,  (Spain). 

Fig.  24.  Graphic  comparison  of  the  profile  type  with  the  Rio 
Lozoya  Dam,  (Spain). 

Fig.  2  5.  Graphic  comparison  of  the  profile  type  with  the  Alicante 
Dam,  (Spain). 

Fig.  26.  Graphic  comparison  of  the  profile  type  with  the  Ternay 
Dam,  (France). 

Fig.  27.  Graphic  comparison  of  the  profile  type  with  the  Habra 
Dam,  (Algiers). 

Fig.  28.  Graphic  comparison  of  the  profile  type  with  the  Nijar 
Dam,  (Spain). 

Fig.  29.  Graphic  comparison  of  the  profile  type  with  the  Elcho 
Dam,  (Spain). 

Fig.  30.  Graphic  comparison  of  the  profile  type  with  the  Gros- 
bois  Dam,  (France). 

Fig.  31.  Graphic  comparison  of  the  profile  type  with  the  Bos- 
me*lea  Dam,  (France). 

Fig.  32.  Graphic  comparison  of  the  profile  type  with  the  Lampy 
Dam,  (France). 

Fig.  33-  Graphic  comparison  of  the  profile  type  with  the  Glomel 
Dam,  (France). 


SUMMARY. 


Fig.  34.     Graphic  comparison  of  the  profile  type  with  the  Vioreau 
Dam,  (France). 


In  figures  2 1  to  34  inclusive  the  parts  shaded  thus 


belong  to  the  profile  types  ;  those  shaded  thus 


belong 


to  the  structure  given,  but  are  outside  of  the  profile  type  ;  those  not 
shaded  are  common  to  both. 


STUDY    ON    RESERVOIR   WALLS. 


TABLE   la. 

GIVING   IN   FEET   THE   PRINCIPAL   DIMENSIONS    OF 
RESERVOIR    WALLS. 


Depth 
of  the 
water. 

Height 
of  the 
first 
step. 

Width 
on  top. 

Height 
of  top 
above 
the 
water. 

VERSED  SINE. 

BATIR   OF 
PEDESTAL. 

RADIUS  OF 
CURVATURE. 

Total 
width  of 
the  base. 

Up- 

Down- 

Up- 

Down- 

Up- 

Down- 

stream. 

stream. 

stream. 

stream. 

stream. 

stream. 

H 

H> 

AB 

BC 

DN 

LM 

GF 

IK 

R 

R' 

IF 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

feet. 

16.40 
32.81 

6.56 

8.20 

1.64 
3-28 

3-28 
6.56 

3-28 

8.20 

42.65 
85-30 

42.65 
69.72 

13.12 

22.96 

49-21 
65.62 

9.84 
11.48 

Jig 

9.84 

13.  J2 

14.76 
22.97 

127.96 
170.61 

89.41 
105.22 

34-44 
47-57 

82.02 

13.12 

8.20 

16.40 

32.81 

213.26 

118.94 

62.34 

98.43 

14.76 

9.84 

19.69 

44.29 

255-91 

78.75 

114.83 

16.40 

11.48 

22.97 

57.42 

298.56 

I43-54 

96.79 

131.24 

16.40 

16.40 

11.48 

22.97 

57-42 

10.94 

16.40 

298.56 

J43.54 

130.69 

147.64 

32.81 

16.40 

11.48 

22.97 

57-42 

21.87 

32.81 

298.56 

143.54 

158.04 

164.04 

49.21 

16.40 

11.48 

22.97 

57-42 

32.81 

49.21 

298.56 

M3-54 

185.38 

TABLE   Ib. 

GIVING   IN    METRES    THE   PRINCIPAL   DIMENSIONS  OF 
RESERVOIR  WALLS. 


Depth 
of  the 
water. 

Height 
of  the 
first 
step. 

Width 
on  top. 

Height 
of  top 
above 
the 
water. 

VERSED  SINE. 

B^TIR  OF 
PEDESTAL. 

RADIUS   OF 
CURVATURE. 

Total 
width  of 
the  base. 

Up- 

Down- 

Up- 

Down- 

Up- 

Down- 

stream. 

stream. 

stream. 

stream. 

stream. 

stream. 

H 

H> 

AB 

BC 

DN 

LM 

GF 

IK 

R 

R> 

IF 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

metres. 

5.00 

2.00 

0.50 

1.  00 

i  .00 

13.00 

13.00 

4.00 

IO.OO 

2.50 

1.  00 

2.OO 

2.50 

26.00 

21.25 

7.00 

15.00 

3.oo 

1.50 

3.00 

4-50 

39-oo 

27-25 

10.50 

20.00 
25.00 

3-50 
4.00 

2.00 
2.50 

4.00 
S-oo 

7.00 

IO.OO 

52.00 
65.00 

32.07 
36.25 

14.5° 
19.00 

30.00 

4-50 

3.00 

6.00 

13.50 

78.00 

40.08 

24.00 

35-00 

5.00 

3-50 

7.00 

17.50 

91.00 

43-75 

29.50 

40.00 

S-oo 

5-oo 

3-50 

7.00 

17.50 

3-33 

S-oo 

91.00 

43-75 

39-83 

45-oo 

10.00 

5.00 

3-5° 

7.00 

I7-5° 

6.67 

IO.OO 

91.00 

43-75 

48.17 

50.00 

15.00 

S-oo 

3-50 

7.00 

17-50 

10.00 

15.00 

91.00 

43-75 

56-50 

OFTHB     -$3 

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